When we owned cats, they were very interested in The Byrds, to the point of chasing them around the yard. And I’ve seen chimps at the zoo who were really into The Beetles.
Part of the problem with this discussion is that in any particular genre of anything (and particularly music), there is such a wide range of material. What do you mean by “classical”? What do you mean by “rock”? There are some pieces of classical music and composers that I really like. For instance, I absolutely love Beethoven. But, there are some pieces that I can’t stand, especially if it is really heavy on the violins.
I like a lot of rock, but mostly like an eclectic mix of things. I love Trans-Siberian Orchestra.
The other problem with this discussion is that you haven’t really defined “intelligence”, either. That is a completely separate discussion for GD.
And one more thing about Mahler … he had a lovely wife named Alma, who had been linked romantically with Walter Gropius and Franz Werfel. So apparently, “intelligent” people might not have the same taste in music, but they might have the same taste in women.